This doesn't mean that it's more secure to keep your coins in an exchange.
When you withdraw your coins from an exchange, you usually need to confirm the withdrawal with your email. But what if you the email service doesn't allow to access your email for any reason?
What if the exchange shut down and run away with your money? What if they block your account?

Note that when you put your money on an exchange, you don't have full control over your fund. When you want to withdraw, you actually ask them to process your withdrawal.
When you put your money on a non-custodial wallet, you have full control over coins.